the width of a rectangle is w centimeters. the length of this rectangle is three times its width. the perimeter of the rectangle is greater than 64 centimeters. give the inequality that represents all possible values of w?

Answer 1

Let's set up an inequality to represent all possible values of the width (w) of the rectangle given the information provided.

The length of the rectangle is three times its width, so the length (L) can be expressed as L = 3w.

The perimeter (P) of a rectangle is given by the formula: P = 2(L + w).

The perimeter is greater than 64 centimeters, so we have P > 64.

Now, substitute the expression for L from step 1 into the perimeter formula from step 2:

P = 2(3w + w)

Simplify the expression inside the parentheses:

P = 2(4w)

P = 8w

Now, we have the perimeter in terms of the width: P = 8w.

We already know that P > 64, so we can write the inequality:

8w > 64

To isolate w, divide both sides of the inequality by 8:

w > 64 / 8

w > 8

So, the inequality representing all possible values of the width (w) is:

w > 8

This means that the width of the rectangle must be greater than 8 centimeters for the perimeter to be greater than 64 centimeters.